Continue with the version of the two-period consumption model discussed in question 1. Suppose that y and y remain at their original values, but r increases from 0.2 to 0.5. (a) What is the consumer's lifetime wealth now? Using the formula for logarithmic preferences, find the new optimal levels of current consumption, future consumption and saving. (b) Using a graph, plot/illustrate the changes in consumption and saving. Be sure to indicate by how much the budget line shifts (horizontally and vertically). (c) Based on the changes you found in parts (a) and (b), in this model is the income effect of an interest rate change stronger or weaker than the substitution effect? Continue with the version of the two-period consumption model discussed in question 1. Suppose that y and y remain at their original values, but r increases from 0.2 to 0.5. (a) What is the consumer's lifetime wealth now? Using the formula for logarithmic preferences, find the new optimal levels of current consumption, future consumption and saving. (b) Using a graph, plot/illustrate the changes in consumption and saving. Be sure to indicate by how much the budget line shifts (horizontally and vertically). (c) Based on the changes you found in parts (a) and (b), in this model is the income effect of an interest rate change stronger or weaker than the substitution effect